Does a creature with first strike and deathtouch kill a creature with regular combat damage if it survives first strike damage?

Combat damage is dealt in two steps when first strike (or double strike) is involved. In the first combat damage step, only creatures with first strike or double strike assign damage. In the second combat damage step, creatures that don't have first strike (or do have double strike) assign damage. A creature with both first strike and deathtouch participates only in the first step, not the second (CR 702.2b, 702.7b).

Deathtouch means that any amount of damage that creature deals to another creature is enough to destroy it (CR 702.2c). So if the first strike/deathtouch creature deals even 1 damage to the opposing creature in the first damage step, that creature will be destroyed before the second damage step ever occurs — meaning the opposing creature never gets to deal its combat damage back.

However, your question asks the reverse: if the enemy creature somehow survives the first strike damage step (for example, it has indestructible, or the first strike/deathtouch creature was tapped or lost its abilities), the first strike/deathtouch creature does NOT deal damage again in the second step unless it also has double strike. It dealt its damage already and is done.

Concrete example: Your 1/1 with first strike and deathtouch attacks into an opponent's 4/4 with indestructible. In the first combat damage step, your 1/1 deals 1 damage to the 4/4. Because the 4/4 is indestructible, it survives. In the second combat damage step, the 4/4 deals 4 damage to your 1/1, destroying it — and your 1/1 deals no further damage because it only has first strike, not double strike.

So the short answer: a first strike + deathtouch creature usually kills the blocker before the second damage step, but if the blocker survives first strike damage for any reason, the first strike/deathtouch creature does NOT deal damage again in the regular damage step and the blocker can deal its damage normally.